Bayesian model selection without evidences: application to the dark energy equation-of-state

TL;DR

The paper introduces a Bayesian model selection method that avoids explicit evidence calculations by using a combined likelihood and a model selection parameter, simplifying the process especially for dark energy models.

Contribution

A novel Bayesian model selection approach that bypasses evidence computation, applicable to dark energy equation-of-state analysis using MCMC or nested sampling.

Findings

ΛCDM model is strongly favored over extensions

Method effectively compares multiple models without evidence calculation

Application to dark energy models demonstrates practical utility

Abstract

A method is presented for Bayesian model selection without explicitly computing evidences, by using a combined likelihood and introducing an integer model selection parameter $n$ so that Bayes factors, or more generally posterior odds ratios, may be read off directly from the posterior of $n$. If the total number of models under consideration is specified a priori, the full joint parameter space $(\theta, n)$ of the models is of fixed dimensionality and can be explored using standard Markov chain Monte Carlo (MCMC) or nested sampling methods, without the need for reversible jump MCMC techniques. The posterior on $n$ is then obtained by straightforward marginalisation. We demonstrate the efficacy of our approach by application to several toy models. We then apply it to constraining the dark energy equation-of-state using a free-form reconstruction technique. We show that $\Lambda$CDM is significantly favoured over all extensions, including the simple $w(z){=}{\rm constant}$ model.